Consider the following statements : I. If $ n \times n $ ($ n 1 $) matrix is symmetric, then its inverse is also a symmetric matrix. II. If $ n \times n $ ($ n 1 $) matrix is singular, then its adjoint is also a singular matrix. Which of the statements given above is/are correct ?

Question

Consider the following statements : I. If $ n \times n $ ($ n > 1 $) matrix is symmetric, then its inverse is also a symmetric matrix. II. If $ n \times n $ ($ n > 1 $) matrix is singular, then its adjoint is also a singular matrix. Which of the statements given above is/are correct ?

SquadPrep · Accepted Answer

Both I and II. Statement I is correct because (A^-1)^T = (A^T)^-1 = A^-1. Statement II is correct because for a singular matrix |A| = 0, and |adj(A)| = |A|^(n-1) = 0.

Answer

I only

Answer

II only

Answer

Neither I nor II

Consider the following statements : I. If \( n \times n \) (\( n > 1 \)) matrix is symmetric, then its inverse is also a symmetric matrix. II. If \( n \times n \) (\( n > 1 \)) matrix is singular, then its adjoint is also a singular matrix. Which of the statements given above is/are correct ?

Explanation

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